what will be the expected real rate of interest for an account that offers a 12% nominal rate of return when the rate of inflation is 6% annualy ?
The correct answer and explanation is:
The expected real rate of interest can be calculated using the Fisher equation, which relates nominal interest rates, real interest rates, and inflation. The Fisher equation is: (1+nominal rate)=(1+real rate)(1+inflation rate)(1 + nominal \, rate) = (1 + real \, rate)(1 + inflation \, rate)
Given that:
- Nominal rate = 12% or 0.12
- Inflation rate = 6% or 0.06
You can substitute these values into the Fisher equation: (1+0.12)=(1+real rate)(1+0.06)(1 + 0.12) = (1 + real \, rate)(1 + 0.06)
Simplifying the equation: 1.12=(1+real rate)(1.06)1.12 = (1 + real \, rate)(1.06)
Now, divide both sides by 1.06 to isolate the real rate: 1.121.06=1+real rate\frac{1.12}{1.06} = 1 + real \, rate 1.0566≈1+real rate1.0566 \approx 1 + real \, rate
Subtract 1 from both sides: real rate≈0.0566real \, rate \approx 0.0566
So, the real rate of return is approximately 5.66%.
Explanation
The nominal rate of interest is the stated rate that you earn on an account or investment before considering the effects of inflation. In this case, the nominal rate is 12%. However, inflation erodes the purchasing power of money, meaning the actual return (real return) is less than the nominal rate.
The Fisher equation provides a way to adjust for inflation and determine the real rate of return. By using this equation, you account for the impact of inflation on your investment. In this case, with an inflation rate of 6%, the real return is lower than the nominal rate.
After solving the equation, you find that the real rate of interest is approximately 5.66%, which reflects the true growth of your investment in terms of purchasing power, accounting for the effect of inflation.